topics on ideals

Below is a list of main concepts in the part of ring theory concerning ideals:

• ideal (http://planetmath.org/Ideal)

• zero ideal

• proper ideal

• ideal of elements with finite order

• modular ideal

• regular ideal

• nil ideal

• nilpotent ideal

• primitive ideal

• primary ideal

• semiprime ideal

• prime ideal, minimal prime ideal

• characterization of prime ideals

• large ideal

• maximal ideal

• maximal ideal is prime

• comaximal ideal

• principal ideal

• finitely generated ideal (http://planetmath.org/EntriesOnFinitelyGeneratedIdeals)

• ideal generated by

• sum of ideals

• product of ideals

• quotient of ideals

• ideal multiplication laws

• product of finitely generated ideals

• ideal included in union of prime ideals

• ideals contained in a union of ideals

• dense ideals/subsets of a ring

• cancellation ideal

• radical ideal

• fractional ideal of commutative ring

• integral ideal

• invertible ideal

• invertibility of regularly generated ideal

• inverse ideal

• generators of inverse ideal

• ideal generators in Prüfer ring

• ideal inverting in Prüfer ring

• fractional ideal (integral domain)

• image ideal of divisor

• ideals in a Dedekind domain